Can Ensemble Variance Predict Representation Error?

Data Assimilation schemes combine observational data with a short term model forecast to produce an analysis.  However, many characteristics of the atmospheric states described by the observations and the model differ.  Observations often measure a higher resolution state than coarse resolution model grids can describe. Hence, the observations may measure aspects of gradients or unresolved eddies that are poorly resolved by the filtered version of reality represented by the model.  This inconsistency, known as observation representation error, must be accounted for in data assimilation schemes.  We explore here the ability of the ensemble to predict the variance of the observation error of representation.  We explore this predictive relationship using differences between model states and their spectrally filtered form, as well as commonly used statistical methods to estimate observation error variances.  We demonstrate that the ensemble variance is a useful predictor of the observation error variance of representation and that it could be used to account for flow dependence in the observation error covariance matrix.